Final answer:
In an elastic collision between two billiard balls of equal masses moving with equal speeds, when they hit head-on and their directions are both reversed, their speeds after the collision will remain the same.
Step-by-step explanation:
In an elastic collision between two billiard balls of equal masses moving with equal speeds, when they hit head-on and their directions are both reversed, their speeds after the collision will remain the same. The conservation of momentum states that the total momentum before the collision is equal to the total momentum after the collision, as long as no external forces act on the system. Since the masses and speeds are the same for both balls, their speeds will remain unchanged.